/*
* Trackball code:
*
* Implementation of a virtual trackball.
* Implemented by Gavin Bell, lots of ideas from Thant Tessman and
*   the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129.
*
* Vector manip code:
*
* Original code from:
* David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli
*
* Much mucking with by:
* Gavin Bell
*/

#include <cmath>
#include "Trackball.h"

/*
* This size should really be based on the distance from the center of
* rotation to the point on the object underneath the mouse.  That
* point would then track the mouse as closely as possible.  This is a
* simple example, though, so that is left as an Exercise for the
* Programmer.
*/
#define TRACKBALLSIZE  (0.8)

/*
* Local function prototypes (not defined in trackball.h)
*/
static float TbProjectToSphere(float, float, float);
static void NormalizeQuat(float [4]);

void VZero(float *v)
{
	v[0] = 0.0;
	v[1] = 0.0;
	v[2] = 0.0;
}

void VSet(float *v, float x, float y, float z)
{
	v[0] = x;
	v[1] = y;
	v[2] = z;
}

void VSub(const float *src1, const float *src2, float *dst)
{
	dst[0] = src1[0] - src2[0];
	dst[1] = src1[1] - src2[1];
	dst[2] = src1[2] - src2[2];
}

void VCopy(const float *v1, float *v2)
{
	register int i;
	for (i = 0 ; i < 3 ; i++)
		v2[i] = v1[i];
}

void VCross(const float *v1, const float *v2, float *cross)
{
	float temp[3];

	temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
	temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
	temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
	VCopy(temp, cross);
}

float VLength(const float *v)
{
	return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
}

void VScale(float *v, float div)
{
	v[0] *= div;
	v[1] *= div;
	v[2] *= div;
}

void VNormal(float *v)
{
	VScale(v,1.0/VLength(v));
}

float VDot(const float *v1, const float *v2)
{
	return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
}

void VAdd(const float *src1, const float *src2, float *dst)
{
	dst[0] = src1[0] + src2[0];
	dst[1] = src1[1] + src2[1];
	dst[2] = src1[2] + src2[2];
}

/*
* Ok, simulate a track-ball.  Project the points onto the virtual
* trackball, then figure out the axis of rotation, which is the cross
* product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
* Note:  This is a deformed trackball-- is a trackball in the center,
* but is deformed into a hyperbolic sheet of rotation away from the
* center.  This particular function was chosen after trying out
* several variations.
*
* It is assumed that the arguments to this routine are in the range
* (-1.0 ... 1.0)
*/
void Trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
{
	float a[3]; /* Axis of rotation */
	float phi;  /* how much to rotate about axis */
	float p1[3], p2[3], d[3];
	float t;

	if (p1x == p2x && p1y == p2y) {
		/* Zero rotation */
		VZero(q);
		q[3] = 1.0;
		return;
	}

	/*
	* First, figure out z-coordinates for projection of P1 and P2 to
	* deformed sphere
	*/
	VSet(p1,p1x,p1y,TbProjectToSphere(TRACKBALLSIZE,p1x,p1y));
	VSet(p2,p2x,p2y,TbProjectToSphere(TRACKBALLSIZE,p2x,p2y));

	/*
	*  Now, we want the cross product of P1 and P2
	*/
	VCross(p2,p1,a);

	/*
	*  Figure out how much to rotate around that axis.
	*/
	VSub(p1,p2,d);
	t = VLength(d) / (2.0*TRACKBALLSIZE);

	/*
	* Avoid problems with out-of-control values...
	*/
	if (t > 1.0) t = 1.0;
	if (t < -1.0) t = -1.0;
	phi = 2.0 * asin(t);

	AxisToQuat(a,phi,q);
}

/*
*  Given an axis and angle, compute quaternion.
*/
void AxisToQuat(float a[3], float phi, float q[4])
{
	VNormal(a);
	VCopy(a,q);
	VScale(q,sin(phi/2.0));
	q[3] = cos(phi/2.0);
}

/*
* Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
* if we are away from the center of the sphere.
*/
static float TbProjectToSphere(float r, float x, float y)
{
	float d, t, z;

	d = sqrt(x*x + y*y);
	if (d < r * 0.70710678118654752440) {    /* Inside sphere */
		z = sqrt(r*r - d*d);
	} else {           /* On hyperbola */
		t = r / 1.41421356237309504880;
		z = t*t / d;
	}
	return z;
}

/*
* Given two rotations, e1 and e2, expressed as quaternion rotations,
* figure out the equivalent single rotation and stuff it into dest.
*
* This routine also normalizes the result every RENORMCOUNT times it is
* called, to keep error from creeping in.
*
* NOTE: This routine is written so that q1 or q2 may be the same
* as dest (or each other).
*/

#define RENORMCOUNT 97

void AddQuats(float q1[4], float q2[4], float dest[4])
{
	static int count=0;
	float t1[4], t2[4], t3[4];
	float tf[4];

	VCopy(q1,t1);
	VScale(t1,q2[3]);

	VCopy(q2,t2);
	VScale(t2,q1[3]);

	VCross(q2,q1,t3);
	VAdd(t1,t2,tf);
	VAdd(t3,tf,tf);
	tf[3] = q1[3] * q2[3] - VDot(q1,q2);

	dest[0] = tf[0];
	dest[1] = tf[1];
	dest[2] = tf[2];
	dest[3] = tf[3];

	if (++count > RENORMCOUNT) {
		count = 0;
		NormalizeQuat(dest);
	}
}

/*
* Quaternions always obey:  a^2 + b^2 + c^2 + d^2 = 1.0
* If they don't add up to 1.0, dividing by their magnitued will
* renormalize them.
*
* Note: See the following for more information on quaternions:
*
* - Shoemake, K., Animating rotation with quaternion curves, Computer
*   Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
* - Pletinckx, D., Quaternion calculus as a basic tool in computer
*   graphics, The Visual Computer 5, 2-13, 1989.
*/
static void NormalizeQuat(float q[4])
{
	int i;
	float mag;

	mag = (q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
	for (i = 0; i < 4; i++) q[i] /= mag;
}

/*
* Build a rotation matrix, given a quaternion rotation.
*
*/
void BuildRotMatrix(float m[4][4], float const q[4])
{
	m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
	m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
	m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
	m[0][3] = 0.0;

	m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
	m[1][1]= 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
	m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
	m[1][3] = 0.0;

	m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
	m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
	m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
	m[2][3] = 0.0;

	m[3][0] = 0.0;
	m[3][1] = 0.0;
	m[3][2] = 0.0;
	m[3][3] = 1.0;
}

